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User blog:King2218/BAL Notation Part 4
Let's make the numbering system of both the ARRAY and the LEVEL the same. It's a bit complicated right now. Intro In Part 3, googleaarex mentioned something called a Mega n-bal which is: \text{Mega n-bal} = n(\underbrace{n, n, \cdots, n}_{n})\{0\} It gave me the basis on a multidimensional LEVEL. (I can't really think of anything to make the ARRAY multidimensional but meh) I tried to make multiple LEVELs but ended up just making them compact by storing them inside a multidimensional LEVEL that contains SEPARATORS. Things got complicated and I decided to shift the numbering system of the ARRAY and the SEPARATORS into something more reasonable. Here is an example of how to evaluate: 2(0,111)\{0\} * = 2(2,011)\{0\} * = 2(211)\{0\} * = 2(111)\{2,2\} * = 4(111)\{1,2\} * = 4\uparrow\uparrow4(111)\{0,2\} * = 4\uparrow\uparrow4(011)\{4\uparrow\uparrow4,1\} * = 4\uparrow\uparrow4(\underbrace{4\uparrow\uparrow4, 4\uparrow\uparrow4, \cdots}_{4\uparrow\uparrow4}10)\{4\uparrow\uparrow4,1\} * = 4\uparrow\uparrow4(\underbrace{4\uparrow\uparrow4, 4\uparrow\uparrow4, \cdots}_{4\uparrow\uparrow4})\{4\uparrow\uparrow4,1\} Indeed, this is very large. If you didn't get the process, read along. After the last step shown above, the BASE becomes (4\uparrow\uparrow4)\uparrow^{(4\uparrow\uparrow4) + 1}(4\uparrow\uparrow4) . If you're curious about the +1 on the number of arrows, it's because I changed the numbering system so I have to add one to get the right amount of arrows. Let's look at the rules. Even More Rules Let \# and \#^* represent rest of ARRAY/LEVEL. For \# , there MUST be a rest of ARRAY/LEVEL but for \#^* , it's optional. Let a , b , c , and d be COUNTING NUMBERS. Let ' 0 ' be ' , '. * a(0)\{0\} = a (You'll notice the shift in the numbering system here) * a(\#)\{\#, 0\} = a(\#)\{\#\} * a(\#)\{\underbrace{0, 0, \cdots, 0}_{n}, b, \#^*\} = a(\#)\{\underbrace{a, a, \cdots, a}_{n}, b - 1, \#^*\} * a(c \#^*)\{0\} = a(c-1 \#^*)\{\underbrace{a, a, \cdots, a}_{a}\} * a(\underbrace{0, 0, \cdots, 0}_{n}, c \#)\{\#\} = a(\underbrace{a, a, \cdots, a}_{n}, c - 1 \#^*)\{\#\} * a(c \#^*)\{b, \#^*\} = a\uparrow^{c+1}a(c \#^*)\{b - 1, \#^*\} * a(\# - 1 0)\{\#\} = a(\#)\{\#\} * a(\#, 0 d \#)\{\#\} = a(\# d \#)\{\#\} * a(0 d_1 \cdots 0 d_n c, \#^*)\{\#\} = a(\underbrace{a - 1 \cdots - 1 a}_{a} d_1 \cdots * \cdots \underbrace{a - 1 \cdots - 1 a}_{a} d_n c - 1, \#^*)\{\#\} Three new rules. The last two bullets are just one rule. You can see how fast this grows by examining the example earlier. LARGE, right? And that's just 1 . Numbers Megabal Group * \text{Mega Unibal} = 1(0 1 1)\{0\} * \text{Mega Bibal} = 2(0 1 1)\{0\} * \text{Mega Tribal} = 3(0 1 1)\{0\} * \text{Mega Quadribal} = 4(0 1 1)\{0\} * \text{Mega Decabal} = 10(0 1 1)\{0\} * \text{Mega King Bal} = 2218(0 1 1)\{0\} * \text{Mega Balgong} = 100000(0 1 1)\{0\} Megablex Group * \text{Unimegablex} = \text{Mega Unibal}(0 1 1)\{0\} * \text{Bimegablex} = \text{Mega Bibal}(0 1 1)\{0\} * \text{Trimegablex} = \text{Mega Tribal}(0 1 1)\{0\} * \text{Quadrimegablex} = \text{Mega Quadribal}(0 1 1)\{0\} * \text{Decamegablex} = \text{Mega Decabal}(0 1 1)\{0\} * \text{King Megablex} = \text{Mega King Bal}(0 1 1)\{0\} * \text{Megablexigong} = \text{Mega Balgong}(0 1 1)\{0\} Megadublex Group * \text{Unimegadublex} = \text{Unimegablex}(0 1 1)\{0\} * \text{Bimegadublex} = \text{Bimegablex}(0 1 1)\{0\} * \text{Trimegadublex} = \text{Trimegablex}(0 1 1)\{0\} * \text{Quadrimegadublex} = \text{Quadrimegablex}(0 1 1)\{0\} * \text{Decamegadublex} = \text{Decamegablex}(0 1 1)\{0\} * \text{King Megadublex} = \text{King Megablex}(0 1 1)\{0\} * \text{Megadublexigong} = \text{Megablexigong}(0 1 1)\{0\} Hyperbal Group * \text{Hyper Unibal} = 1(1 1 1)\{0\} * \text{Hyper Bibal} = 2(0 2 2)\{0\} * \text{Hyper Tribal} = 3(0 3 3)\{0\} * \text{Hyper Quadribal} = 4(0 4 4)\{0\} * \text{Hyper Decabal} = 10(0 10 10)\{0\} * \text{Hyperior Bal} = 2218(0 2218 2218)\{0\} * \text{Hyper Balgong} = 100000(0 100000 100000)\{0\} Hyperblex Group * \text{Unihyperblex} = \text{Hyper Unibal}(0 Unibal} \text{Hyper Unibal})\{0\} * \text{Bihyperblex} = \text{Hyper Bibal}(0 Bibal} \text{Hyper Bibal})\{0\} * \text{Trihyperblex} = \text{Hyper Tribal}(0 Tribal} \text{Hyper Tribal})\{0\} * \text{Quadrihyperblex} = \text{Hyper Quadribal}(0 Quadribal} \text{Hyper Quadribal})\{0\} * \text{Decahyperblex} = \text{Hyper Decabal}(0 Decabal} \text{Hyper Decabal})\{0\} * \text{Hyperior Blex} = \text{Hyperior Bal}(0 Bal} \text{Hyperior Bal})\{0\} * \text{Hyperblexigong} = \text{Hyper Balgong}(0 Balgong} \text{Hyper Balgong})\{0\} Hyperdublex Group * \text{Unihyperdublex} = \text{Unihyperblex}(0 \text{Unihyperblex} \text{Unihyperblex})\{0\} * \text{Bihyperdublex} = \text{Bihyperblex}(0 \text{Bihyperblex} \text{Bihyperblex})\{0\} * \text{Trihyperdublex} = \text{Trihyperblex}(0 \text{Trihyperblex} \text{Trihyperblex})\{0\} * \text{Quadrihyperdublex} = \text{Quadrihyperblex}(0 \text{Quadrihyperblex} \text{Quadrihyperblex})\{0\} * \text{Decahyperdublex} = \text{Decahyperblex}(0 \text{Decahyperblex} \text{Decahyperblex})\{0\} * \text{Hyperior Dublex} = \text{Hyperior Blex}(0 Blex} \text{Hyperior Blex})\{0\} * \text{Hyperdublexigong} = \text{Hyperblexigong}(0 \text{Hyperblexigong} \text{Hyperblexigong})\{0\} More Extensions? Of course there are but I'm going to post them when I feel like it. For now, don't expect a new part to come out! Oh and... The rules were hard... Did I miss a rule? Is a rule wrong? Comment about it! Category:Blog posts